Explanation
First $$15$$ positive odd numbers will be,
$$1,3,5,7,9,\dots$$
We can observe that these numbers are in A.P.
The sum of first $$n$$ terms of an A.P whose first term is $$a$$ and common difference is $$d$$ can be written as, $$S_n = \dfrac{n}{2} [2a + (n - 1)d].$$
From the series of first positive odd numbers we can conclude that, $$a=1$$ and $$d=2.$$
Substitute the values of $$a,\ d$$ and $$n$$ in the formula of sum of first $$n$$ terms of an A.P,
$$\begin{aligned}{}{S_{15}} &= \frac{{15}}{2}[2 \times 1 + (15 - 1)2]\\& = 7.5[2 + 14\times2]\\& = 7.5[2 + 28]\\ &= 7.5[30]\\& = 225\end{aligned}$$
So, the sum of the first $$15$$ positive odd numbers of the A.P. is $$225.$$
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